U.S. Department of Commerce

National Bureau of Standards

NBS MEASUREMENT SERVICES

Special Publication 250-33

A Calibration Service for

Voltage Transformers and

Higli-Voitage Capacitors
INTRODUONG THE CENTER FOR ELECTRONICS AND ELECTRICAL ENGINEERING

The Center for Electronics and Electrical Engineering (CEEE) is the confiponent of the

National Bureau of Standards charged with providing Bureau activities and services

supporting electrotechnology. In response to identified and anticipated needs, Center

programs provide national reference standards, measurement methods, supporting theory and

data, and traceabiiity to national standards. Beneficiaries are U.S. industry, other

Government organizations, the academic community, and society at large. In fiscal year

1987, the Center calibrated nearly a thousand transfer standards for some 200 customers.

The Center is organized into four technical divisions, with the Electrosystems and

Semiconductor Electronics Divisions at Gaithersburg, Maryland and the Electromagnetic

Fields and Electromagnetic Technology Divisions at Boulder, Colorado. The Center

provides measurement research and services for:

o Conducted electrical signals and energy in the Electrosystems Division:

- dielectrics for advanced power systems

- conducted electromagnetic interference

- waveform synthesis

- signal acquisition and processing

- automatic test equipment

- calibration/testing strategies

o Radiofrequency signals and interference in the Electromagnetic Fields Division:

- radiofrequency to millimeter-wave electromagnetic fields and signals

- general microwave and millimeter-wave instruments, components

microwave and millimeter-wave noise

microwave and millimeter-wave antenna systems

radiated electromagnetic interference; electromagnetic compatibility

monolithic microwave/millimeter-wave integrated circuits

- materials properties measurements at high frequencies

o Lightwaves, cryogenics, and magnetics in the Electromagnetic Technology

Diviston:

- optical fibers; integrated electro-optics

- superconducting materials

- superconducting electronics

- magnetic materials

o Semiconductor electronics, in the Semiconductor Electronics Division:

- semiconductor materials, such as silicon and gallium arsenide

- semiconductor materials modification

- semiconductor devices

- integrated-circuit test structures for rapid process assessment

For information, contact the Center at 1 -301 -975-2220 or write to: The Center for Electronics and Electrical Engineering, Metrology Building Room B-358, National Bureau of Standards, Gaithersburg, MD 20899.
NBS MEASUREMENT SERVICES:

A Calibration Service for

Voltage Transformers and

High-Voltage Capacitors

William E. Anderson

Electrosystems Division

Center for Electronics and Electrical Engineering

National Engineering Lalx)ratory

National Bureau of Standards

Gaithersburg, MD 20899

June 1988

U.S. DEPARTMENT OF COMMERCE, C. William Verity, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
Library of Congress Catalog Card Number: 88-600542

National Bureau of Standards Special Publication 250-33

Natl. Bur. Stand. (U.S.), Spec. Publ. 250-33, 37 pages (June 1988)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1988

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
— PREFACE

( 'alihrat ions and related measurement services of the National Bureau of Standards (NBS) provide

the means for industry, government agencies, ax:aLdemia, and others to relate the measurements

they make to national standards and, by extension, to the measurement systems of other countries

throughout the world. It is of crucial importance to improving U.S. productivity, efficiency, and

quality—in short our competitive stance—that measurements of appropriate ax:curacy can be made

at all stages of product development, production, and marketing and that it is possible to refer the

results of these measurements to each other in a meaningful way. NBS services provide essential support for satisfying these needs, as well as measurement needs arising from societal concerns such

as health, safety, natural resources, and defense. The requirements of NBS clientele range from the

highest levels of accuracy realizable from advanced science and technology to the practical levels of

accuracy needed to support routine production. A reference-level measurement may be the result of days of painstaking individual effort or may be provided by a semi-automatic measuring system

in minutes. The variation in customer needs and hence in NBS services responsive to those needs is great.

The more than 300 different calibration services, measurement assurance services, and special tests that are offered by NBS are described in NBS Special Publication 250, NBS Calibration Services Users Guide. The Guide provides essential technical details of NBS calibration and related measurement services, such as levels of accuracy provided by NBS and the requirements to be met

by customers' transfer standards. It also provides information needed for placing orders for these

services and identifies technical and administrative contacts for each service.

Technical descriptions in the Users Guide are intended to be restricted to the material needed

by a potential customer to decide if a given service will meet that customer's needs. Frequently, a customer may be interested in more detailed and extensive information, such as the way in which the

errors dissociated with a measurement are assessed. Beginning in 1987, NBS established a Special

Publication 250 series which supplements the Guide. Each publication in this series provides a

detailed technical description of a specific NBS calibration service, or closely related set of services,

and includes:

• specifications for the service

• design philosophy and theory

• description of NBS measurement system used to provide service

• NBS operational procedures

• measurement uncertainty assessment, including error budget, identification of systematic and

random errors

• NBS internal quality control procedures

Special Publication 250-33, A Calibration Service for Voltage Transformers and HighVoltage Capacitors, describes services offered under NBS Test Numbers 545I0C through 54513C

(voltage transformers) and 52400C (high-voltage capacitors at power frequency). These services are provided by the Applied Electrical Measurements Group in the Electrosystems Division as part of a series of services offered by the Division in support of the transmission and distribution of electric powerv

iii

Table of Contents

1 INTRODUCTION 1

2 RANGE OF SERVICES 3

2.1 Voltage Transformers 3

2.2 Capacitors 4

3 MEASUREMENT METHODOLOGY 5

3.1 Basic Measurement Circuits 5

3.2 Capacitors 6

3.3 Voltage Transformers 8

4 MEASUREMENT INSTRUMENTATION 14

5 MEASUREMENT UNCERTAINTIES 21

5.1 Voltage Transformers 21

5.2 Capacitors 23

6 ACKNOWLEDGMENTS 24

7 REPORT FORMAT 24

APPENDIX 27

REFERENCES 30

V
List of Figures

1 Schering bridge 2

2 Basic measurement circuit for the calibration of a high-voltage capacitor 5

3 Basic measurement circuit for the calibration of a voltage transformer 6

4 Basic measurement circuit for the 4-terminal calibration of large capacitors 7

5 Correct measurement circuit for the calibration of a voltage transformer 9

6 A voltage transformer measurement circuit with a wiring defect 10

7 A voltage transformer measurement circuit with a wiring defect 10

8 An improved measurement circuit for the calibration of voltage transformers 11

9 Equivalent circuit of a voltage transformer 12

10 Equivalent circuit of a voltage transformer with secondary burden 13

11 Capacitive burden box 13

12 Basic current comparator bridge 15

13 Current comparator bridge with high-voltage resistor for in-phase current balance. . 16

14 Current comparator with superior in-phase current balance 16

15 Current comparator bridge modified for 4-terminal capacitance measurements. ... 18

16 Current comparator bridge with external range extender 19

17 Circuit for checking operation of dissipation factor measurement of current comparator bridge 20

18 Circuit for determining correction to measurement shown in figure 17 21

vi
List of Tables

1 Measurement Capability 3

2 Gas Density Dependence 8

3 ANSI Standard Burdens 12

4 Check Standard History 18

5 Dissipation Factor Check Standard 22

6 Contributions to Uncertainty 23

7 Total Estimated Uncertainties 23

vii
r
A Calibration Service for Voltage Transformers

and High-Voltage Capacitors

William E. Anderson

Abstract

The National Bureau of Standards calibration service for voltage transformers and high-voltage

capacitors is described. The service for voltage transformers supports the measurement of ratio correction factors and phase angles at primary voltages up to 170 kV and secondary voltages

as low as 10 volts at 60 Hz. Calibrations at frequencies from 50-400 Hz are available over a more limited voltage range. The service for high-voltage capacitors supports the measurement

of capacitances and dissipation factors at applied voltages ranging from 100 V to 170 kV at 60 Hz depending on the nominal capacitance. Calibrations over a reduced voltage range at other frequencies are also available. As in the case with voltage transformers, these voltage

constraints are determined by the facilities at the National Bureau of Standards.

Key words: calibration; capacitors; dissipation factor; electric power; electric standards; NBS

services; voltage transformers

1 INTRODUCTION

The purpose of this report is to provide a description of the National Bureau of Standards (NBS)

methodology for calibrating high-voltage capajcitors and transformers. It is hoped that this might

benefit the customers in several ways. First, by understanding how NBS makes these measurements,

the customers might be able to define weaknesses in their own measurement procedures and correct them. Secondly, the customers might be able to make better use of the data in the calibration report

(e.g., to understand what is meant by the uncertainty statement). Thirdly, the customers might be

able to better specify the required test conditions so that information more pertinent to their needs

might be obtained at a lesser cost.

This report describes two different calibration services: high-voltage capacitors and voltage trans- formers. At NBS these two services are performed using the same equipment. In fact, in order to calibrate a voltage transformer, one of the steps is to measure the ratio of two capacitors. The two

services are therefore discussed in parallel.

There are several different ways to measure the ratio and phase angle of a voltage transformer. Harris [1] categorizes them as the direct versus comparative methods and within these two classifications either the deflection or null measurement technique. A direct measurement is defined here to mean

a measurement in which the quantity of interest can be determined without a comparison to some

absolute standard.

In the "direct deflection method" the primary and secondary voltage vectors are each directly

measured. This approach is, in general, of most value for lower voltage transformers (i.e., primary

voltages of order 100 volts). Even then m.ore accurate, less difficult measurements can be made using one of the other techniques.

1
Figure 1. Schering bridge.

In the past NBS had used a "comparative null method" to calibrate voltage trajisformers. The

unknown transformer was compared to an NBS reference transformer using a voltage comparator

consisting of a variable resistive divider and a mutual inductor. Reference transformers were available

with ratios ranging from 1/1 up to 2000/1. Measurement uncertainties in the comparison of the

unknown transformer with the reference transformer were ±0.01% for ratio and ±0.3 minutes for phase angle. The ratio and phase angle of the reference transformers were known to about the same accuracy. There are several disadvantages to this approach. Since the comparator has a

limited range, several reference transformers must be available to cover the anticipated users' needs.

The ratio and phase angles of each one of these transformers must be carefully determined over

the secondary voltage range of interest. These transformers then have to be rechecked at regular

intervals to determine if the ratios and phase angles have changed.

If a direct measurement method were available that was sufficiently accurate and straightforward to make the calibration of these reference transformers a simple task, then that method could be used

to measure the customer's transformer directly. At NBS, the "direct null method" in use originally

involved balancing the secondary of the reference transformer against the output of a resistive divider used in conjunction with a variable mutual inductor to provide phase angle balance. Such a measurement was difficult because the resistive divider ratio changed with heating. Since the late 1960's a "direct null method" has been available that is straightforward and accurate and is now

used at NBS in place of comparative methods using reference transformers.

Capacitors are invariably measured by balancing the unknown capacitor against a known standard

using some type of bridge arrangement. There are a variety of such bridges described in the lit- erature [2]. The one most used in high-voltage applications in the last sixty years is the Schering

bridge (figure 1). Two high-voltage arms of this bridge consist of the standard and unknown capacitors. The two low voltage arms are resistors (one has a parallel capacitor for phcise angle balance).

2
The main limitation of the Schering bridge is a result of the fact that the low side of the unknown

and standard capax;itors are not at ground potential at bridge balance. Therefore, without careful guarding of the bridge components, stray currents can affect the bridge accuracy. The voltage

applied to the shields to eliminate these stray currents must be adjusted for both magnitude and

phase. Unfortunately this procedure is not perfect and bridge accuracy is consequently affected. Another limitation of the Schering bridge is the inherent inaccuracy of the resistance ratio of the

two low-voltage arms. The current comparator bridge developed by Kusters and Petersons [3] allows the intercomparison

of two capacitors with their low-voltage terminals at ground potential, thereby eliminating the

main objection in using the Schering bridge. This bridge used in both the voltage transformer

and capacitor calibrations will be described in some detail in Section 4. There is an important

distinction between the calibration of voltage transformers and capacitors at NBS. The voltage

transformer calibration is of the direct null type, and the capacitor calibration is of the comparative

null type. In other words, the accuracy of the capacitance measurements ultimately depends on the

uncertainty in assigning a value to a standard capacitor. The standard capacitor used in this service

is directly traceable to the calculable cross capacitor [4] which, in turn, is known in terms of the

fundamental unit of length.

The remainder of this document is divided into the following subject areas: voltage transformers

and capacitors covered by this service, measurement methodology, measurement instrumentation,

analysis of uncertainties, and calibration report format. The contents of this document plus the cited references should provide the reader with a fairly complete description of the voltage transformer

and high-voltage capacitor calibration service at NBS.

2 RANGE OF SERVICES

The NBS measurement capabilities are summarized in table 1 and discussed in more detail below.

Table 1. Measurement Capability

Voltage Transformers - 60 Hz

Primary Voltage Secondary Voltage Phase Angle

50-170,000 Vrms > 50 V rms < 1 1 mrad

Capacitors - 60 Hz

Applied Voltage^ Capacitance Dissipation Factor 50-170,000 Vrms lOpF - O.OOIF < 0.011

2.1 Voltage Transformers

Presently, voltage transformers (assuming they are of sufficient quality to be used as laboratory

standards) with primary voltages up to 170 kV at a frequency of 60 Hz can be calibrated at NBS. This

maximum voltage is imposed by the supply transformer and not by limitations in the measurement

instrumentation. Therefore, this constraint should not be considered rigid and customers should

contact the NBS about present physical limitations.

The largest portion of the voltage transformers submitted to NBS are calibrated with a total esti- mated uncertainties of ±300 ppm in ratio, and ±0.3 mrad in phase angle. These transformers are

^ Total power must be less than 50kVA.

3
of sufficient quality to be considered transfer standards. Historically these transformers have shown

excellent long-term stability rarely changing by more than 100 ppm in ratio or O.lmrad in phase

(at or below rated burden) for periods as long as thirty years or more. In general the voltage and

burden dependence of these transformers are the major contributors to the measurement uncertainties. These uncertainties (±300 ppm for ratio, ±0.3mrad for phase angle) meet the accuracy

requirements of most of our customers.

Voltage transformers of a higher accuracy class often serve as transfer standards for manufacturers

of voltage transformers and voltage transformer test sets (voltage comparators). The estimated

uncertainties for these transformers are ±100 ppm in ratio, and ±0.1 mrad in phase angle. They are generally designed for use with very small burdens (< 15 volt-amperes).

The above discussion for voltage transformers assumes a voltage at a frequency of 60 Hz. The

National Bureau of Standards has some capability to calibrate voltage transformers from about

50 Hz to 400 Hz (at the lower voltage and power ranges). Such calibrations are infrequent and

customers interested in these voltage ranges and measurement uncertainties should contact NBS

directly.

2.2 Capacitors

The maximum voltage for capa<:itor calibrations is presently 170 kV at 60 Hz. The restrictions is imposed by the supply transformer and not by limitations in the measurement instrumentation.

Therefore, this constraint should not be considered time invariant and customers should contact NBS about present physical limitations.

The maximum power available is 50kVA (i.e., C < 50, 000/{27r60V^} where V is the applied voltage

and C is the capacitance). In order to energize the capacitors a resonant circuit is often required to couple the necessary energy into the customer's capacitor. Since this requires the availability of an

assortment of series and parallel inductors and capacitors, there are undoubtedly some capacitors

that, despite having a burden of less than 50 kVA, cannot be calibrated. The customer should contact NBS before submitting a capacitor for calibration. As with voltage transformers, NBS restricts its calibration services to those devices of sufficient quality to be used as the transfer standards. This

in general depends upon the stability of the capacitor (i.e., whether the measured capacitance and

dissipation factor are intrinsic properties of the device itself or instead are largely a function of

conditions at the time of the calibration). For example, small two-terminal capacitors (less than

10,000 picofarads) may be significantly influenced by stray capacitance in the measurement circuit. There are cases, however, where one component (capacitance or dissipation factor) is stable and the

other is not. For example, power factor capacitors often have relatively stable dissipation factors but have capacitances that vary significantly with applied voltage (even demonstrating hysteresis

effects) and temperature. In this case a calibration of dissipation factor would be meaningful. It also is important that the capacitors have connectors^ that are generally available, e.g., BNC, GR,

UHF, BPO, or Type N. The most accurate capacitor calibrations have an uncertainty of ±25 ppm for capacitance and an

uncertainty of ±5 x 10~^ for dissipation factor. For capacitors with large dissipation factors, the

dissipation factor uncertainty is generally at least ±1% of the measured value ±5 x 10~^. The

uncertainty in the capacitance value and the dissipation factor can be largely a function of the

stability of the capacitor.

^Certain commercial products are identified. In no case does such identification imply recommendation by NBS,

nor does it imply the products cire the best available.

4
V

Cx

Nd Cs

Nx ^-n=r^ Ns

Figure 2. B«isic measurement circuit for the calibration of a high-voltage capacitor.

3 MEASUREMENT METHODOLOGY

3.1 Basic Measurement Circuits

The current comparator bridge used to calibrate voltage transformers and high-voltage capacitors

will be discussed in considerable detail in Section 4. A brief discussion of this bridge will be presented

here in order to facilitate understanding of the NBS measurement methodology. A simplified circuit for meeisuring the ratio of two capacitors is shown in figure 2. (The active circuitry to achieve

dissipation factor balance is not included). At balance

V2TrfC^N^ V2wfCsN,

Nd

where f is the frequency. This can be rewritten

(1)

C -^c (2)

The simplified circuit for measuring the ratio of voltage transformers is shown in figure 3. At balance

Vp2nfCpNr _ Vs2nfC,N,

Nd Na

or,

(3)

(4)

The ratio of the two capacitors in (2) can be measured using the circuit discussed above in figure 2.

The measurement of a voltage transformer or a capacitor both involve the measurement of the ratio of two standard capacitors. The measurement of capacitors will be discussed below followed by a

discussion on the measurement of voltage transformers.

5
Vp

Figure 3. Basic measurement circuit for the calibration of a voltage transformer.

3.2 Capacitors

General Measurement Technique

Capacitors are measured by balancing the current through the capax:itor under test against the

current through a standard air or compressed gas capacitor as shown in figure 2. Large capacitors

(> 1 microfarad) necessitate a four-terminal measurement as shown in figure 4. A discussion of this measurement will be discussed in Section 4. The four-terminal measurement does eliminate the

effect of the leads in the measurement of the capacitance and dissipation.

Information Necessary to Initiate Calibration

The customer usually only needs to specify the voltage and the frequency. For small capacitors

(10,000 picofarads or less), it is essential that the low-voltage electrode and the conductor leading

to the measurement instrumentation be shielded by a grounded conductor. Otherwise, the stray

capacitance may cause significant measurement error. The National Bureau of Standards requires some sort of standard connector (BNC, UHF, GR, BPO, or Type N) at the low-voltage terminal

in order to connect to the measurement system. Larger capacitors do not need to be shielded but

must be measured as a four terminal admittance because of the non-negligible lead impedance.

A description of how this measurement is done will be covered in Section 4. Capacitors must be

stable and reproducible in order to be considered standards, and, hence, warrant an NBS calibration.

Power factor capacitors (large capacitors used to tune distribution lines, etc.) are often special cases. Their dissipation factors (in-phases component of the current divided by quadrature component)

are often quite stable but their capacitance values are often not. Because of the importance of these

capacitors to the electrical industry, they are often acceptable for calibration even though they do

not meet normal stability requirements.

Although the instrumentation has been used to calibrate a million-volt standard capacitor at rated

voltage, the instrumentation does impose some limitations on the voltage applied to the capacitor.

The only limitation on the maximum voltage is that the current through the standard capacitor should be no larger than 10 milliamperes. In order to have reasonable sensitivity, the current

6
V

Nx -±: Ns

Figure 4. Basic measurement circuit for the 4-terminal calibration of large capacitors.

should be at least 10 microamperes. The current through the customer's capacitor can range from

10 microamperes to 1000 amperes.

Voltage Dependence

For the calibration of both capacitors and voltage transformers, the voltage coefficient of the standard

capacitor is important. The unit of capacitance at NBS is maintained at low voltage. This value

must be transferred to the high-voltage standard capacitors at their working voltages. At NBS,

considerable work was done to modify a commercial high-voltage standard capacitor to minimize

its voltage coefficient and to determine the magnitude of that voltage coefficient [5]. The National

Bureau of Standards was able to demonstrate that, if care were taken, a well-designed standard

capacitor should change capacitance by only a few ppm from 0 to 300 kV. A more recent paper also discusses the problem of the voltage dependence of standard capacitors and describes an international

comparison of high-voltage capacitor measurements [6]. (This paper also discusses the effect of

shipping and handling on the measured capacitance of a commercial standard capacitor.) The

voltage dependence of a compressed gas capacitor principally arises from the coulombic attraction

of the two electrodes and is hence quadratic in nature. The capacitor should be expected to vary

only slightly at lower voltages. Therefore, a capacitor rated at 200 kV should be quite effective in measuring the voltage dependence of another capacitor rated at 20 kV.

Temperature Dependence

Another concern is the temperature dependence of the high-voltage standard capacitor. The typical

dependence is about -|-20ppm/°C. This dependence arises solely from the thermal expansion of the

components of the capacitor. Since C is directly proportional to the electrode area and inversely

proportional to the electrode separation, the thermal coefficient of the standard capacitor is pro- portional to the linear coefficient of expansion. Although the laboratories at NBS are fairly stable

in temperature, the comparison of the high-voltage standard capacitor to the low-voltage standard

(which has a thermal coefficient of 2ppm/°C) is done at the beginning and conclusion of the mea7
Table 2. Gas Density Dependence

GAS dC/dP at T = 22.8 °C

(units of picofarads/pascal)

SFe

CO2

He

(2.012 ± 0.022) X 10-^ + [(5.1 ± 0.6) x lO'^^jP

(0.903 ± 0.015) X 10-« + [(1.4 ± 0.4) x lO'^^jp

(0.075 ± 0.004) X 10-6 + [(0.2 ± 0.1) x lO'^^jp

surement process. The average value is then used in order to minimize the problem associated with

this thermal drift.

Gas-Density Dependence

Compressed gas standard capacitors can have an additional source of error associated with gas

leakage. Values of dC/dP (to first order in pressure) measured at a temperature of 22.8 °C are shown in table 2 for three different gases [6]. The gas pressure, P, is in units of pascals and the capacitance in picofarads. For a 100-pF capax;itor

with SFe £is the dielectric gas, a 1-psi (GQOO-pascal) leak would cause the capacitance to decrease by

about 140 ppm. It must be stressed that this change is valid only if the pressure change is caused

by the loss of gas and not by the lowering of the gas temperature. As can be seen in table 2, the

gas density coefficient is largest for SFe- Customers using compressed gas capacitors for standards

might be advised to monitor the gas pressure with a good quality pressure gauge. Leaking SFg-filled

capacitors should be checked often against a good low-voltage standard.

3.3 Voltage Transformers

Information Necessary to Initiate Calibration

In order to calibrate a voltage transformer, several different parameters must be specified: frequency;

windings and/or range; secondary voltage; and burden or impedance across the secondary winding.

In some cases, for example when there is a tertiary winding, additional parameters may be required.

Labeling of Terminals

There are some standard conventions as to which of the primary and secondary taps are to be at low or ground potential and which are to be at rated voltage. Some transformers have one tap of

the secondary and one tap of the primary winding marked by a "i". These two taps are connected

together and to ground potential. Some transformers use the designators HI, H2 for the primary

taps, and XI, X2 (and Yl and Y2 for the transformers with two secondaries) for the secondary taps.

Sometimes the secondary winding has a third tap, X3. By convention the primary and secondary

taps with the largest number are connected together and to ground. If the customer wants some

other arrangement, they should notify NBS prior to the calibration.

Load Imposed by NBS Measurement System

The basic measurement circuit is shown in figure 5. The two capacitors shown are three-terminal

standard capacitors. Their dissipation factors are typically less than 5 x 10-^. The capacitor

connected to the secondary usually has the nominal value of 1000 pF. Therefore, for 60-Hz measurements, the capacitor imposes a negligible load (2.7 megohms or 0.005 volt-amperes at 120 volts) on

the voltage transformer. Negligible in this case means that the effect of this burden on the measured

ratio and phase angle can not be observed at the ppm level. The digital voltmeter (DVM) in figure 5

8
e

BURDEN DVM r~ CURRENT I COMPARATOR

[

BRIDGE I

—

1

::=FCp

L_ _l

Figure 5. Basic measurement circuit for the calibration of a voltage transformer with a digital

voltmeter (DVM) and secondary burden.

has an estimated uncertainty of less than ±0.5% of the reading and measures true-rms ac volts. The internal impedance of the DVM is equal to or greater than a megohm.

Possible Errors Caused by Improper Wiring

The wiring of the circuit shown in figure 5 is critical. For example, it is important that the two

capacitors be connected directly to the primary and secondary terminals of the transformer. Consider

instead figure 6. The capacitor C is connected to the burden and the DVM instead of directly to the secondary terminal of the transformer. If the secondary burden were an ANSI standard burden

ZZ (36 ohms at 120 volts, see table 3) and the resistance of the lead connecting the burden to the

transformer were lOmilliohms, the incorrect wiring shown in figure 6 would cause an error in the

transformer ratio measurement of about 0.03%. For higher impedance burdens this becomes less of a problem but, in general, one must take precautions to avoid including the voltage drop in the

lead connecting the transformer to the burden as part of the voltage on the transformer secondary

winding to be measured.

Another major concern in the measurement of the ratio and phase angle of a voltage transformer

is the proper definition of the ground point and the avoidance of ground loops. This can best be

illustrated by the presentation of a few examples. In figure 7, some common mistakes are shown.

The transformer is energized in such a manner that significant current is forced to flow between

the transformer ground and the circuit ground. The resulting voltage drop in the lead connecting

the transformer and ground will be part of the ratio and phase angle measured. The high-voltage

capacitor is not connected directly to the primary of the transformer under test. The measurement

of the ratio and phase angle, therefore, includes the eff'ect of the voltage drop in the lead between

the point where the capacitor is connected to the power source and the transformer. In addition,

as there are three different "ground" points in the circuit and it is not, in general, possible to know

the voltages and impedances between these points, a measurement error is probable.

In figure 8 the problem has been eliminated by defining the low-voltage terminal of the transformer

as ground. Although this point may significantly differ from the building or utility ground, from

the measurement point of view this is the correct ground. It is important that the shields of the

9
e

1

BURDEN DVM

Cs

CURRENT

-\ COMPARATOR r

I BRIDGE I

I

Cp

Figure 6. Measurement circuit for the calibration of a voltage transformer. Connection of low-voltage

capacitor as shown is incorrect.

BURDEN DVM I CURRENT I

] COMPARATOR

p

I BRIDGE I

I ^ I

Figure 7. Measurement circuit for the calibration of a voltage transformer. Grounds are poorly

defined.

10
e

BURDEN DVM I CURRENT

! COMPARATOR

I BRIDGE

_l

Figure 8. Measurement circuit for the calibration of a voltage transformer. Measurement ground is defined. Transformer excitation current flows from the measurement ground to building ground.

three-terminal capacitors, the bridge detector ground, and all other measurement grounds each be

connected directly to this point.

In figure 5 the preferred method of wiring a voltage transformer calibration circuit is shown. The

customer's transformer is connected in such a way that the energizing current does not flow between

the transformer and the measurement ground. All measurement grounds are connected to the

transformer ground point. The two capacitors are connected directly to the primary and secondary

terminals of the transformer. Only one ground is used in the circuit. While it is not always possible

to connect the transformer as in figure 5, this is the best choice. Otherwise tests are required to ensure that systematic errors are not compromising the measurement results. Burdens

The burden attached to the secondary of the customer's transformer (as shown in figure 5) is specified by the customer. In general this would not be the burden corresponding to the maximum

volt-ampere rating of the transformer but instead would be equal to the burden attached to the

transformer in its intended use. For example, if the transformer will only have a digital voltmeter

attached to its secondary, a calibration with a secondary impedance of a megohm would be more

useful than one with an ANSI ZZ burden attached. Since the ANSI burdens are often requested,

they are summarized in table 3 [7]. By convention these burdens are defined for a frequency of 60 Hz

only.

Suhstiiuie Burdens

If the customer does not send the secondary burden with the transformer, the National Bureau of

Standards will provide the burden. It is not practical to have available and adequately characterized

all of the anticipated burdens. Fortunately this is not necessary. If the ratio and phase angle of a

transformer is known for two diff"erent burden values, the ratio and phase angle at any other burden

can be calculated (with certain limitations) [8]. A derivation of the formulas relating the ratios and

phase angles at zero and some other known burden value are given in the appendix and presented

in abbreviated form below.

11
Table 3. ANSI Standard Burdens

ANSI Burden Volt-cimperes Power Fax:tor (Lagging)

W 12.5 0.10

X 25 0.70

M 35 0.20

Y 7 0.85

Z 200 0.85

TL 400 0.85

The voltage transformer will be represented as an ideal transformer with some unknown series output impedance, Zq , as shown in figure 9. The model has been shown to be sufficiently accurate

experimentally. The relationship between the input voltage, Ei , and the output voltage with zero burden, is:

e.-^^" (5)

where N is the nominal (or turns) ratio of the transformer, RCF is the ratio-correction factor (A'^xRCF= actual ratio) at zero burden. To is the angle by which the secondary voltage vector leads

the primary voltage vector and j = \/^. A similar relationship exists between the input voltage,

and the output voltage E^^ with secondary burden C (having impedance Zc) shown in figure 10:

1^- = iVRCF,e-^rc (6)

where RCFc is the ratio correction factor with secondary burden C and Fc is the corresponding

phase angle. If the transformer is measured at zero burden (RCFp and Fo) and at burden T (RCFt

and Ft), the ratio correction factor and phase angle at burden C are approximately given by:

RCFe w RCF„ + |^[(RCFt - RCF,) cos(0t - B,) + (F^ - F<,) sin(0t - (7)

where Be — \./Zc is the burden in ohms~^ of the impedance Zc, and

Tc « F„ + |^[(Ft - F„) cos(^t - 6,) - (RCFt - RCYo)sin{6t - 6^)]. (8)

tin

Ei

E„

12
Figure 10. Equivalent circuit of a voltage transformer with secondary burden

Figure 11. Capacitive burden box.

The power factor of burden C is cos^c? RCFc is the ratio correction factor calculated for burden C,

and Fc is the angle by which the secondary voltage leads the primary voltage for burden C.

The equations (7) and (8) can be used to calculate the RCF and phase angle for some secondary

burden, C, if the ratio correction factors and phase angles are known at some other burden, T, and

at zero burden. In practice, at NBS, capacitive burdens are used for the "T" or known burdens in eqs (7) and (8). The main reason is their stability. The heat generated in a large resistive burden,

for example, is likely to cause the burden's impedance value to vary. Capacitors, in addition, are compact so even the ZZ burden in table 3 is easy to handle. At NBS, capacitive burden boxes have

been constructed in a binary layout (figure 11) so that capacitors from 1 to 32 microfarads can be

switched in and out allowing any capacitance value from zero to 63 microfarads. Since a ZZ burden

is equivalent to a 74 microfarad capacitor at 120 volts, two such burden boxes are sufficient for nearly

all the calibrations at NBS.

Several approximations were made to derive eqs (7) and (8). The approximations relate to the

relative ratio of the transformer's output impedance, Zo, to the impedance of the secondary burden

Zt or Zc. The smaller this ratio, the more accurate are eqs (7) and (8). This ratio also affects the differences, RCFt — RCFq and Fj — Fq. If the ratio correction factor difference is 0.001 or less, and if the phase angle difference is 1 milliradian or less than eqs (7) and (8) should be accurate to within ilOppm for the ratio correction factor and to within ±10 microradians for the phase angle

if it is assumed that the ratio of the burdens is known with no more than ail percent uncertainty.

Data over the years has indicated that eqs (7) and (8) are always at least that accurate. In order

to identify any problems, an extra measurement is made at a different secondary burden to test the

13
predictive capabilities of eqs (7) and (8) for the transformer under test. If a problem is discovered,

the error budget is adjusted accordingly.

The above discussion might enable customers of the voltage transformer calibration service to better

design their calibration requests. Using eqs (7) and (8), the customer might be able to reduce the

number of measurements required. A note of caution is in order. It is likely that using a zero burden

and a 10 volt-ampere burden result to predict the transformer's behavior at a ZZ burden may lead

to large inaccuracies. The reasons are twofold. First, the differences RCFj — RCFq and Fj — F^ are

likely to be small for a burden as small as 10 volt-amperes and extrapolations can cause large errors. The second reason can be seen from figure 10. The higher current of the ZZ burden will cause Zq to heat up and increase in value, leading to errors if eqs (7) and (8) are used. Somewhat better results are likely if one used a ZZ burden result to predict a transformer's behavior at 10 volt-amperes.

However, it is best to choose burden, T, to have a volt-ampere rating the same order of magnitude

as the burden of interest, C. Also, the values in eqs (7) and (8) are all to be measured at the same

frequency and at the same secondary voltage.

Harmonic Effects The measurement of the ratio and phase angle of a voltage transformer can be affected by the

presence of harmonics in the voltage waveform. If a tuned null detector is not used, the balance

of a bridge circuit can be difficult in the presence of harmonics and often a precise balance is not

possible resulting in increased measurement uncertainties. Harmonics can also lead to errors in measuring the magnitude of the secondary voltage. For example, if an average reading, rms scaled

voltmeter measured a 100-volt rms fundamental with an in- phase 3- volt rms third harmonic, the

meter would read 101 volts. Setting the voltage to read 100 volts on the meter would result in a one

volt discrepancy between the intended and actual voltage. Many transformers have large enough

voltage c6efficients for this one-volt error in the voltage setting to have a non-negligible effect on

the measured ratio correction factor and phase angle. If instead, a true rms voltmeter were used

to measure this signal, the measured voltage would be 100.045 volts and the resulting error would

be negligible. At NBS three different steps are taken to lessen the effects of harmonics. The first

is to try to minimize the harmonic content of the power supply. The supply used for most of the

calibrations has a total harmonic distortion of order 0.2 % of the fundamental. Second, a tuned

detector is used to assure that the balance conditions are for the fundamental component of the

voltage waveform. And third, all voltage measurements are made witli true-rms voltmeters.

Voltage Dependence of Standard Capacitor

An additional measurement concern is the voltage coefficient of the high-voltage standard capacitor

shown in figure 5. Although no absolute measurements are required to calibrate a voltage trans- former, the ratio of the two standard capacitors must be known. The problem is that the low-voltage

standard capacitor typically has a maximum voltage rating of 500 volts, and both the primary of

the transformer and the high-voltage standard capacitor might be energized to 100 kV. Since the

capacitor ratio measurement must be done at less than 500 volts, the voltage dependence of the

high-voltage capacitor is important. This problem was discussed in Section 3.2.

4 MEASUREMENT INSTRUMENTATION

The calibration of voltage transformers and high-voltage capacitors at NBS requires the combined

use of standard capacitors and the current comparator bridge. Standard capacitors have been

thoroughly discussed in the literature [5, 6, 9]. The care that must be taken with their use in these

types of measurements has been discussed above. The current comparator bridge will be discussed

in this section.

14
V

\/lx

Nd

\^ Is

Figure 12. Basic current comparator bridge.

The current comparator bridge can be thought of as a voltage comparator transformer arm bridge

in which the detector and power source have been interchanged. Traditionally, the disadvantage of

the current comparator bridge versus the voltage comparator bridge is the signal-to-noise level. For

high-voltage measurement applications, this is no longer a problem. Kusters and Petersons were the

first to develop this bridge for the comparison of two capacitors at high voltage [3]. A basic current comparator bridge is shown in figure 12. The current in the unknown capacitor, Cx, is balanced

against the current in the standard capacitor, C,, by varying the turns ratios, A'^, and NxBalance is achieved when the signal at the detector, D, is equal to zero. At balance IxNx = Is^s

or:

The bridge shown in figure 12 has no means of balancing the in-phase current resulting from a

non-ideal unknown capacitor, Cx- The current comparator in figure 13 does have the capability of

balancing both the in-phase and quadrature components of the capacitive current. The difficulty

with the approach used in figure 13 is that the applied high voltage is across the variable resistance

R,. It is nearly impossible to design a stable high-voltage variable resistor with negligible phase

defect. Another means is necessary to balance the in-phase current, preferably at low voltage using

well-characterized components.

The current comparator shown in figure 14 provides a satisfactory means of achieving both the

in-phase and quadrature current balances. The quadrature current balance is identical to that in figures 12 and 13 above. The in-phase current balance is accomplished at low voltage with the aid

of an operational amplifier. The current from the standard capacitor after passing through the N,

winding goes to the inverting input of the operational amplifier. This point is at virtual ground

so the capacitive current balance, eq (10), is not affected. The feedback capacitor, Cj, causes the

output voltage of the operational amplifier to be a small fraction {Cs/Cj where Cfis approximately

10 /iF) of the applied voltage and tt radians out of phase with it. The inductive voltage divider allows a known fraction, a, of this output signal to be applied across a standard resistor, R. As can be

seen from figure 14, the signal is first inverted before the resistor in order to have the correct phase

'•elationship with the unknown in-phase current. It is necessary that the non-inverted signal be

VlnfCxNx = V2TrfCsNs

where / is the frequency. This balance equation can also be expressed as:

(9)

(10)

15
V

Cx

D

Nd

Nx

,_rrvr\ ^

Ns

Cs

Is

Figure 13. Current comparator bridge with high-voltage resistor for in-phase current balance.

V

Figure 14. Current comparator with superior in-phase current balance.

16
applied to an identical standard resistor as shown in figure 14 so that the current from the standard

winding, N,, reaching the operational amplifier hcis no phase defect. The in-phase current into the

standard winding, N,, is then equal to:

/R. (11)

Since the quadrature current lout = V2irfCt, the dissipr.tion factor is: DF=^= (12)

lout 2irfRVCfC, ^ ^

or

The resistor, R, can be chosen so that a is direct rezwling in percent or millirswlians.

In some Ccises, particularly for larger capacitors, it is necessary to make a four-terminal measure- ment. This is required when the lead and winding impedances become a significant fraction of the

impedance to be measured. Figure 15 shows a current comparator bridge with this capability. Because of the non-negligible lead and winding impedance, there is some voltage, e, at the low- voltage

terminal of the capacitor. This voltage signal is inverted as shown in figure 15 and connected to the

Ns winding through a capacitor, Cgi. The current through the unknown capacitor is: h = j2TrfiV - e)Q (14)

The current reaching the winding is:

Is=j27rfVCs-j2nfeCs'. (15)

If Cs' is adjusted prior to the measurement to be equal to C, then eq (15) reduces to:

Is=j2nf{V-e)C,. (16)

Comparing this with eq (14), the eff'ect of the compensation circuit has been to place the same

voltage across both the standard and unknown capacitors. This is exactly what is required for lead

compensation.

Figure 16 shows the last enhancement of the bridge to be discussed. The National Bureau of

Standards' current comparator bridge has an internal range of 1000:1 (i.e., the maximum value of

Nd/Nx is 1000). The external current transformer shown in figure 16, referred to as a range extender,

increases the measurement range by a factor of 1000 allowing the comparison of two currents diff"ering in magnitude by as much as a factor of a million. As with the transformers internal to the current comparator bridge, the accuracy requirements on the range extender are quite stringent. Further

details on the design of a ppm current comparator and the specifics of NBS' current comparator

bridge are available in the literature [10, 11]. The current comparator bridge is quite straightforward to use and has proven to be rugged in practice. In order to monitor the behavior of NBS' current comparator bridge, a check standard is maintained. In this case, the check standard consists of two high quality standard capacitors. The

ratio of the two capacitors is measured quarterly. For the last seven years, this ratio has been stable to within 20 ppm as can be seen in table 4. The drift can readily be attributed to the two capacitors. The 9 ppm change between 10/84 and 4/85

occurred apparently after one of the capacitors had been used for another purpose. An independent

measurement of that capacitor verified the change. While the use of this check standard cannot

17
V

Figure 15. Current comparator bridge modified for 4-terminal capacitance measurements.

Table 4. Check Standard History

Date Capacitance Ratio Date Capacitance Ratio

6/80 1.000025 1/84 1.000032

6/81 1.000028 5/84 1.000033

9/81 1.000027 10/84 1.000032

1/82 1.000027 4/85 1.000041

4/82 1.000026 6/85 1.000042

7/82 1.000026 10/85 1.000041

9/82 1.000028 12/85 1.000042

1/83 1.000030 1/86 1.000041

3/83 1.000031 5/86 1.000044

6/83 1.000033 7/86 1.000044

8/83 1.000031 10/86 1.000044

12/83 1.000031 2/87 1.000044

18
V

Cx

-1>H(-

Cs'

D

Nd

LAAAJ

Nx

Figure 16. Current comparator bridge with external range extender.

19
V

a

Cx Cs

I CURRENT I i COMPARATOR h

I BRIDGE j -JLT

Figure 17. Circuit for checking operation of dissipation factor measurement of current comparator

bridge.

prove that the bridge is still working to the ppm level, it can alert the user of changes large enough

to affect calibration results. Of course, since the two capacitive currents are largely balanced using

stable passive components (i.e., transformer windings), one expects that the bridge should be stable.

It should be noted that if a transformer winding were to become open or short circuited the result would be dramatic and readily observed by the operator.

The situation with the dissipation factor (or in-phase current) balance is different as active components play an important role. Also, it is difficult to design a stable dissipation factor standard to act

as a check standard. This problem has been overcome by using the circuit in figure 17. Standard

capacitors are connected to the standard and unknown sides of the bridge. The known in-phase

current is applied with the use of the inductive voltage divider and a resistor as shown. The advantage of this circuit is that the voltage across the resistor is small (~ 0.3 volt). However, because of

the small voltage, any error voltage, e, at the low side of the resistor, R, becomes important. The

in-phase current entering the A^^ winding is:

liu = aV-e

R

(17)

where a is the ratio of the inductive voltage divider {a <C 1). The dissipation factor lin/Iout is then

equaJ to: aV - e DF =

[{V -£)R27rfC^

(18)

The effect of £ can be significant at the ppm level and needs to be eliminated. The circuit in figure 18

is identical to that in figure 17 except that the input of the inductive voltage divider is grounded.

The dissipation factor in this case is then:

DF„

(V - e)R2nfC^

(19)

20
V

(X

Cx Cs

1^ CURRENT ^

H COMPARATOR V

I BRIDGE I -JLT

Figure 18. Circuit for checking operation of dissipation factor measurement of current comparator

bridge. Input is grounded in order to measure e in eq (18).

Since e ^V subtracting eq (19) from eq (18) one obtains:

DF^ = DF-DF. = ^^. (20)

At NBS typical values of a are 0.003, 0.0003, -0.0003, -0.003. With a one-megohm resistor and a 1000-pF standard capaxzitor this enables a near full scale test of the dissipation factor on its four ranges. Recent results are shown in table 5. The dissipation factor values are all in units of percent.

Agreement between the calculated values in eq (20) and the corrected measurement DFm (the last two columns) are well within ±0.1% of the measured value. This check is performed at approximately six-month intervals.

It is further proposed that an additional check standard be obtained and measured quarterly. Specifically, a voltage transformer measured regularly at a ratio of 10:1 would give an additional check on

the phase angle circuitry and on the bridge windings at something other than a 1:1 ratio.

5 MEASUREMENT UNCERTAINTIES

5.1 Voltage Transformers

The records of the National Bureau of Standards show examples of voltage transformers that have

been calibrated at five-year intervals over a period of thirty to forty years. Invariably the original

uncertainty statement covers any variation in ratio correction factor and phase angle observed over

this period of time. Voltage transformers are often used by the customer in conjunction with other

equipment to measure some quantity. For example, used with a current transformer and watthour

meter, a voltage transformer can help provide a measure of the energy consumed by a large power

21
Table 5. Dissipation Factor Check Standard

Measured Correction Corrected Theoretical

Date a (DF) (DFo) {DFm) {a/2nfRC^)

7/82 0.0003 0.08003 0.0002 0.07983 0.07977

0.003 0.7982 0.0002 0.7980 0.7977

-0.003 -0.7979 0.0002 -0.7981 -0.7977

-0.0003 -0.07959 0.0002 -0.07979 -0.07977

3/83 0.0003 0.08135 -0.00014 0.08149 0.08147

0.003 0.81455 -0.00015 0.8147 0.8147

-0.003 -0.81475 -0.00015 -0.8146 -0.8147

-0.0003 -0.08160 -0.00014 -0.08146 -0.08147

10/83 0.0003 0.'J7952 -0.0001 0.07962 0.07959

0.003 0.7959 -0.0001 0.7960 0.7959

-0.003 -0.7960 -0.0001 -0.7959 -0.7959

-0.0003 -0.07965 -0.0001 -0.07955 -0.07959

1/84 0.0003 0.08174 0.00029 0.08145 0.08143

0.003 0.8148 0.00029 0.8145 0.8143

-0.003 -0.8140 0.00029 -0.8143 -0.8143

-0.0003 -0.08110 0.00029 -0.08139 -0.08143

5/84 0.0003 0.08090 0.0002 0.08070 0.08071

0.003 0.8076 0.0002 0.8074 0.8071

-0.003 -0.8071 0.0002 -0.8073 -0.8071

-0.0003 -0.08050 0.0002 -0.08070 -0.08071

11/84 0.0003 0.08000 0.0000 0.08000 0.07997

0.003 0.8000 0.0000 0.8000 0.7997

-0.003 -0.8000 0.0000 -0.8000 -0.7997

-0.0003 -0.08000 0.0000 -0.08000 -0.07997

4/85 0.0003 0.08060 0.0000 0.08060 0.08059

0.003 0.8056 0.0000 0.8056 0.8059

-0.003 -0.8055 0.0000 -0.8055 -0.8059

-0.0003 -0.08050 0.0000 -0.08050 -0.08059

12/85 0.0003 0.08070 -0.0001 0.08080 0.08071

0.003 0.8076 -0.0001 0.8077 0.8071

-0.003 -0.8076 -0.0001 -0.8075 -0.8071

-0.0003 -0.08070 -0.0001 -0.08060 -0.08071

11/86 0.0003 0.08029 -0.00022 0.08051 0.08046

0.003 0.8049 -0.00022 0.8051 0.8046

-0.003 -0.8054 -0.00022 -0.8052 -0.8046

-0.0003 -0.08067 -0.00022 -0.08045 -0.08046

22
Table 6. Contributions to Uncertainty

Uncertainties

Random Systematic

Bridge measurement ±2 (±2) ±75 (±25)

Secondary voltage setting ±50 (±10)

Burden setting ±50 (±10)

Transformer self-heating ±75 (±20)

Capacitance ratio measurement ±2 (±2) ± 5 (± 5)

Table 7. Total Estimated Uncertainties

Ratio correction factor ±0.03 % (±0.01 %)

Phase Angle ±0.3mrad (±0.1mrad)

transformer. Thus it is important to the customers of this calibration service to obtain a meaningful

uncertainty statement that reflects the contribution the voltage transformer would make to their total error budget.

As mentioned earlier in this report, voltage transformers calibrated at NBS generally fall into two

accuracy classes: ±0.03 % uncertainty for ratio correction factor, ±0.3 mrad for phase angle; and

±0.01% for ratio correction factor, ±0.1 mrad for phase angle. While it would be possible in some

cases to report smaller uncertainties to the customers by more thorough determinations of such

parameters as voltage coefficients, proximity effects, and burden dependencies, the present service

provides an economical way to present meaningful error statements to the customers and meets their needs.

The analysis of the uncertainties for the ratio correction factor measurements are summarized in table 6. The units are in ppm. The values in parentheses apply to the higher accuracy voltage

transformers described in Section 2.1 above. The uncertainties for the phase angle measurement of voltage transformers are the same as is shown in table 6 except the units are microradians instead

of ppm.

To calculate the uncertainties reported to the customer, the systematic uncertainties tabulated

above are algebraically summed and added to three times the root sum of squares of the random

uncertainties. The results are shown in table 7. The values in table 6 are approximate. Some transformers demonstrate stronger voltage dependences

than others or stronger burden dependences. In some cases the values in table 7 must be adjusted

for such transformers. The purpose of the above tables is to give the users an idea of the sources of

errors and how they are used to calculate an uncertainty statement.

Since most of the sources of error presented in table 6 originate from the transformer under test, NBS could in principle measure a nearly ideal voltage transformer to much better accuracy than

shown in table 7. Such a test would be expensive because of the time-consuming care that would

be required.

5.2 Capacitors

The National Bureau of Standards has the capability to measure the ratio of two capacitors to an

estimated systematic error of ±1 ppm and ±1 x 10~^ ± 1 % of the measured value for the relative dissipation factor. The values of the standard capacitors used for these comparisons are known to

23
±10ppm for capacitance (±1 x 10~^ for dissipation factor). The random error associated with the

capax:itance measurement is ±lppm and ±1 x lO"^ for dissipation factor. Conservatively then,

NBS could calibrate a customer's capacitor to an overall uncertainty of ±15ppm in capacitance and

±5 X 10"^ ± 1 % of the value for dissipation factor. In general, the quoted uncertainty is always

larger than this except for low-voltage standard capacitors similar to those used at the National

Bureau of Standards. (Low-voltage standard capacitors are in general calibrated by the National

Measurement Laboratory of NBS. The service described here provides higher voltage calibration of

these same capacitors).

The uncertainty statements for high-voltage standard capacitors and power-factor capacitors depend

on the stability of these devices during the course of the NBS' measurements. The stability is influenced by both the voltage dependence of the device and self-heating (i.e., the capacitance and

dissipation factors vary as the internal energy dissipated heats the device). Self-heating effects are more important for power-factor capacitors. Some power-factor capacitors demonstrate significant

hysteresis effects. Assigning an uncertainty statement to these measurements depends on the specific

behavior of the capacitor. If self-heating is a problem the calibration report clearly must specify

the amount of time the capacitor was energized before the measurement was made. If hysteresis

effects are detected they are so noted. Because of the nature of most of these devices, the calibration

reports for capacitors usually include a statement of the form: "the estimated uncertainties quoted

apply to the above tabulated values and should not be construed as being indicative of the long-term

stability of the device under test." This statement is also important for the compressed gas insulated

capacitors whose values might change significantly by handling during shipping.

The actual uncertainty quoted to the customer is derived by algebraically summing the systematic

uncertainties and adding three times the root mean sum of squares of the random uncertainties. For

the capacitance measurement of compressed gas insulated capacitors, the measurement uncertainty

will include a 20 ppm contribution because of the possible one kelvin variation in temperature of

the NBS voltage transformer laboratory. For power-factor capacitors the self-heating variations will dominate ambient temperature effects.

6 ACKNOWLEDGMENTS

The author would like to thank Oskars Petersons, Chief of the Electrosystems Division, who has

been the source of nearly all the author's knowledge on the calibration of voltage transformers

and capacitors. The author would also like to acknowledge the work of Barbara Frey and Roberta

Cummings who helped prepare this manuscript. Lastly, but certainly not least, the author would

like to acknowledge both the "old-timers" here at the National Bureau of Standards, who began

the tradition of excellence in measurements, and the present calibration staff who are attempting to carry on this tradition under vastly different constraints.

r REPORT FORMAT

Examples of the calibration report format are shown on the next pages for both the voltage trans- former and high-voltage capacitor calibration service. These formats are frequently modified in order to deal with special circumstances pertaining to a particular calibration.

24
U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

GAITHERSBURG, MD 20899

REPORT OF CALIBRATION

VOLTAGE TRANSFORMER

120-14,400 to 120 Volts, 60 Hertz, 4.4 Volt-Amperes

XXXXX, Serial No. ???????

Submitted by

Customer Name

Customer Address

Frequency Secondary

(hertz) Burden

Secondary

Voltage

(volts)

Phase Angle

Voltage Ratio (milliradian)

60 A

B

120 1 X 1.00001

1.00051

-0.12

-0.16

Date of Test: February 29, 1987

Temperature: 20 °C

The phase angle is positive when the secondary voltage leads the primary voltage of the same

polarity. The characteristics of the burdens designated above are given in the following table:

Impedance

Burden (ohms) Power Factor

A

B

1 X lO'' 576

1.00

1.00

Estimated Uncertainties

Voltage Ratio: ±0.01%

Phase Angle: iO.lmrad

Temperature: ±1 °C

The results given in this report apply to the fundamental frequency components of the voltages.

For the Director

National Engineering Laboratory

Group Leader

Applied Electrical Measurements

Electrosystems Division

25
U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

GAITHERSBURG, MD 20899

REPORT OF CALIBRATION

STANDARD CAPACITOR

XXXXX, Serial No. ???????

Submitted by

Customer Name

Customer Address

Capacitance and dissipation factor were measured on February 29, 1987, at a frequency of 60 Hz. The results are tabulated below.

Ambient Temperature: 21.5 ^'C The dissipation factor was measured to be less than 5 x 10~^.

Estimated Uncertainties

Capacitance: ±0.05 pF

Dissipation Factor: ±5 x 10~®

Temperature: ±1°C

The estimated uncertainties quoted apply to the above tabulated values and should not be construed

as being indicative of the long-term stability of the device under test.

For the Director

National Engineering Laboratory

Group Leader

Applied Electrical Measurements

Electrosystems Division

Voltage

(kilovolts-rms)

Capacitance

(picofarads)

2.55101000.98

1000.98

1000.98

26
APPENDIX

The voltage transformer will be represented as an ideal transformer with some unknown series output impedance, Zq, as shown in figure 9. The model has been shown to be sufficiently accurate

experimentally. The relationship between the input voltage, Ei, and the output voltage with zero burden, Eo, is:

Eo Eo

(21)

where N is the nominal (or turns) ratio of the transformer, RCFo is the ratio-correction factor

(A'^ X RCFo = ax;tual ratio) at zero burden, Tg is the angle by which the secondary voltage vector

leaxis the primary voltage vector and j = y/—l. A similar relationship exists between the input

voltage, Ei, and the output voltage Ec, with secondary burden C (having impedance Zc) shown in figure 10: ^ = iVRCFee--''^^ (22)

En

where RCF,; is the ratio correction factor with secondary burden C and Fc is the corresponding

phase angle.

Equating the current through Zg and Zc in figure 10, one obtains

En Er_ Zo

El

Zr

or E.=

Zo^Zc

This can be rewritten in the following form:

Ec Eo -I

Setting Zo equal to Rg + jXo and Zc equal to Rc + jXc, eq (25) becomes:

Ei_^Ei_ Ro + jXo

Er En

1 +

Rc + jX

Taking the absolute value of both sides of eq (26), one finds that

E. E, RoRc "H XoXc

Ec Eo

1 +

R'' + X}

(23)

(24)

(25)

(26)

(27)

where it has been assumed that both Ro and Xo are much less than Zc so that terms of order

\{RoRc + XoXc)l{R\ + X2)]2 and higher have been neglected. Using eq (21) and (26), one obtains

or

Ei E,

Ec Eo

Ei Ei

e Ec Eo

1 +

Ro + jXo

1 +

Rc + jX,

{Ro + jXo){Rc-jXc)

Rl + X-^ This can also be expressed as Ei E. Ec Eo

(28)

(29)

(30)

27
Both exponentials have arguments much less than one so that discarding quadratic and higher order

terms and equating the imaginary components of the left and right sides of eq (30) one obtains

Ei Ei

Eo

or from eq (25) assuming Zg <C Zc

To XqRc — XcRq

The resistive and reactive components of the burden C can be expressed as

Rc = y/R^Tx^cosOc

and

Xc = y/R^Txjsine,

where cos^c is the power factor of the burden C. From eqs (21) and (22)

Ei

and

Using eqs (27) and (33)-(36) one obtains

RCFc — RCFq

Eo

Ei_

E,

= A^RCFo

= NRCFc

1 4- j—-r{RoCosOc + XosinOc)

(31)

(32)

(33)

(34)

(35)

(36)

(37)

For the purposes of this discussion, it will be assumed that burden C (having impedance Zc) above

is the burden for which the ratio correction factor and phase angle are to be calculated. The ratio- correction factor and phase angle must be known for some other burden, T, which shall be designated

as having impedance, Zt- Using eq (25) and substituting burden T for burden C:

Zo =

EilEt

Ei/Eo

1

or using eq (22)

Zo = ZtiRCFte-^^^'-^"^ - RCF„]/RCFo.

Neglecting second order and higher terms

Zo « ZtiRCFt - RCF, + KTo - FOl/RCFo.

Using the facts that

and

one finds

Zt = \Zt\{coset+jsmet)

Zo = Ro jXo

Ro « (^1^) [(RCFt - RCF„)cos^< + {Vt - To)sm9t]

(38)

(39)

(40)

(41)

(42)

(43)

28
or

and

Xo « (^^) [(ro - r^cos^, + (RCF, - RCF,)sin^,]. (44)

Using eqs (37), (43), and (44) and the relations:

cos 6c cos 6t + sin 6c sin 6t — cos{dt —6c) (45)

cos^csin^t — sin 0c cos = sin(0t — 6c) (46) one finds

RCFc « RCF, + (^g^^jr) [(RCF, - RCF^) cos(0^ - 6c) + (F^ - r„) sin(0, - 6c)] (47)

RCFc « RCF, + ^1^^ [(RCFt - RCF,) cos(0< - 6c) + (Ft - F,) sin(0« - 6c)] (48)

where Be = l/Zc is the burden in ohrns"^ of the impedance Zg. Since the second term in eq (47)

represents a small correction to the first and since RCFq is approximately equal to one, RCFo has

been dropped from the second term of eq (48). Using eqs (32)-(34)

Tc^To- tI-XXoCos6c- Ro sin 6c ) (49)

Using eqs (43)-(46) and (49)

Tc^To+ [j^^^ [(rt - To) cos{6t - 6c) - (RCF, - RCF,,) s\n{6t - 6c)] (50)

or

[{It - Fo) cos{6t - 6c) - (RCF, - RCF,) sin(0, - 6c)] (51)

since RCFo is approximately equal to one. The relations eqs (48) and (51) can be used to calculate the RCF and phase angle for some secondary

burden, C, if the ratio correction factors and phase angles are known at some other burden, T, and

at zero burden.

29
REFERENCES

[1] F. K. Harris, Electrical Measurements, John Wiley & Sons, New York, pp. 576-577 (1966).

[2] F. K. Harris, Electrical Measurements, John Wiley & Sons, New York, pp. 687-738 (1966).

[3] N. L. Kusters and O. Petersons, "A Transformer-Ratio-Arm Bridge for High- Voltage Capacitance Measurements," IEEE Trans. Commun. Electron., vol. CE-82, pp. 606-611, Nov. 1963.

[4] M. C. McGregor, J. F. Hersh, R. D. Cutkosky, F. K. Harris, and F. R. Kotter, "New Apparatus

at the National Bureau of Standards for Absolute Capacitance Measurement," IRE Trans, on

Instrum., vol. 1-7, no. 3 &; 4, Dec. 1958.

[5] D. L. Hillhouse and A. E. Peterson, "A 300-kV Compressed Geis Standard Capacitor with

Negligible Voltage Dependence," vol. IM-22, pp. 406-416, December 1973.

[6] W. E. Anderson, R. S. Davis, O. Petersons, and W. J. M. Moore, "An International Comparison

of High Voltage Capacitor Calibrations," IEEE Trans. Power Appar. Syst., vol. PAS-97, no. 4, pp. 1217-1223, July 1973.

[7] IEEE Standard Requirements for Instrument Transformers, American National Standards Institute, ANSI/IEEE C57.13-1978, pp. 32, 1978.

[8] IEEE Standard Requirements for Instrument Transformers, American National Standards Institute, ANSI/IEEE C57.13-1978, pp. 45, 46, 1978.

[9] F. K. Harris, Electrical Measurements, John Wiley & Sons, New York, pp. 673-687 (1966).

[10] O. Petersons and W. E. Anderson, "A Wide-Range High-Voltage Capacitance Bridge with One

PPM Accuracy," IEEE Trans. Instrum. Meas., vol. IM-24, no. 4, December 1975.

[11] O. Petersons, A Wide-Range High-Voltage Capacitance Bridge with One PPM Accuracy, D.

Sc. dissertation. School of Engineering and Applied Sciences, George Washington University,

Washington, DC, February 1974.

30
NBS-n4A (REV. 2-gC) U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publ Ication Date BIBLIOGRAPHIC DATA

REPORT NO.

SHEET (See instructions) NBS/SP-250/33 June 1988

4. TITLE AND SUBTITLE

A Calibration Service for Voltage Transformers and High-Voltage Capacitors

5. AUTHOR{S)

William E. Anderson

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

National Bureau of Standards

Route 270 and Clopper Road

Gaithersbug, MD 20899

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 88-600542

I I Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or /ess factual summary of most si gnificant information. If document includes a si gnificant

bibliography or literature survey, mention it here) The National Bureau of Standards calibration service for voltage transformers and highyoltage capacitors is described. The service for voltage transformers supports the

meas^urement of ratio correction factors and phase angles at primary voltages up to

170 kV and secondary voltages as low as 10 volts at 60 Hz. Calibrations at frequencies

from 50'-400 Hz are available over a more limited voltage range. The service for highvoltage capacitors supports the measurement of capacitances and dissipation factors at

applied voltages ranging from 100 V to 170 kV at 50 Hz depending on the nominal

capacitance. Calibrations over a reduced voltage range at other frequencies are also

available. As in the case with voltage transformers, these voltage constraints are determined by the facilities at the National Bureau of Standards.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

calibration ; capacitors; dissipation factor; electric power; electric standards;

NBS services; voltage transformers.

13. AVAILABILITY

[x~l Unl imited For Official Distribution. Do Not Release to NTIS

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

37

15. Price

USCOmm-DC 6043-P80

U-U.S. Government Printing Office : 1988 - -597/8:598

THE SP 250 SERIES ON NBS MEASUREMENT SERVICES*

SP 250-1

SP 250-2

SP 250-3

SP 250^

SP 250-5

SP 250-6

SP 250-7

SP 250-8

SP 250-9

Spectral Radiance Calibrations SN003-003-02792-8 $3.50

Far Uitravioiet Detector Standards SN003-003-02810-0 $4.25

Radiometric Standards In the Vacuum

Uitravioiet SN003-003-02806-1 $6.50

Fricke Dosimetry in hIigh-Energy Electron Beams

SN003-003-02816-9 $2.75

Aipha-Partide Calibrations SN003-003^2823-1 $2.00

Regular Spectral Transmittance SN003-00»^2805-3 $3.25

Radiance Temperature Calibrations SN003-003-02827-^ $2.25

Spectral Reflectance SN003-003-02812-6 $7.00

Calibration of Beta-Partide-Emitting

Ophthalmic Applicators

SN003-003-02817-7 $2,00

SP 250-10 Radioactivity Calibrations with the "4ir" Gamma Ionization Chamtwr, and Other

Radioactivity Calibration Capabilities

SN003-003-02824-0 $2.25

SP 250-1 1 Dosimetry for High-Dose Applications

SP 250-12 Neutron Personnel Dosimetry

SN003-003-02811-8 $2.50

SP 250-13 Activation Foil Irradiation with Californium

Fission Sources

SP 250-14 Activation Foil irradiation by Reactor Cavity

Fission Sources SP 250-15 Photometric Calibrations SN003-003-02835-5 $4.25

SP 250-16 Calibration of X-Ray and Gamma-Ray

Measuring Instmments

SP 250-17 The NBS Photodetector Spectral Response

Calibration Transfer Program

SP 250-18 Neutron Source Strength Calibrations

SP 250-19 Calibration of Gamma-Ray-Emttting

Brachytherapy Sources

SP 250-20 Spectral Irradiance Callbratioris SN003-003-02829-1 $5.50

SP 250-21 Calibration of Beta-Partide

Radiation Instrumentation

SP 250-22 Platinum Resistance Thermometer

Calibrations SN003-003-02831-2 $17.00

SP 250-23 UqJd-in-Glass Thermometer

Calibration Sen^

SP 250-24 Standard Cell Calibrations SN003-003-02825-8 $2.75

SP 250-25 Calibration Service for Inductive Voltage Dividers

SP 250-26 Phase Angle Calibrations

SP 250-27 AC-DC Difference Calibrations

SP 250-28 Sdid-State DC Voltage Standard Calibrations SN003-003-02842-8 $2.00

SP 250-29 Traceable Frequency Calilwations SN003-003-02844-4 $2.25

SP 250-30 GOES Satellite Time Code Dissemination:

Description and Operation

SN003-003-02845-2 $2.75

SP 250-31 Mass Calibrations at the National Bireau

of Standards SP 250-32 A Calibration Service for 30 MHz

Attenuation and Ptiase Shift SP 250-33 A Calibration Service for Voltage Transformers and High-Voltage Capacitors

* Those entries containing a stock numtwr (003-003 ) and price can be purchased from the Superintendent of Documents, U.S. Government Printing Offtee, Washington, DC 20402. GPO will accept checks, money orders, VISA, and Mastercharge. For more informatk)n, or to place an order, call (202)783-3238. Be sure to use the stock number in all orders. Titles without stock numbers are in preparatkx).
U.S. Department of Commerce

National Bureau of Standards

Gaithersburg, MD 20899

Official Business

Penalty for Private Use $300

stimulating Americj s Progress 1913-1988